For each of 5 airlines (Airlines 1 through 5), the table shows the per

pre-thinking
- n_k = total ABSOLUTE number of flights last year for the Airline "k" (delayed+not delayed)
- The airlines are numbered from greates total number of flights offered last year to least total number, so:
n_1 > n_2 > n_3 > n_4 > n_5 (inneq. I)
- Let "percentage_k_a_to_b" be the percentage of flights offered by airline "k" last year that were delayed by the range [a,b] minutes (entries of the table)


what is been tested in this question
- your capacity to differentiate relative and absolute size (percentages, innequations)

Statement 1 states that n_2*(9.2%) > n_k*percentage_k_1_to_15, which is not necessarely true, because although 9.2% is the greatest value that percentage_k_1_to_15 can have, maybe n_1 is so big that n_1*8.5% > n_2*9.2%. We cant say whether is true or not. => "Need not be true"

Statement 2 says that n_5*1.2% < n_k*percentage_k_1_to_15, k!=5. This is indeed true because 1.2% < percentage_k_1_to_15, for every k!=5, according with the table, AND we also have that n_5<n_k, for each k!=5, according with "inneq. I". We obtain the original statement by multiplying both innequations. => "Must be true"

Statement 3 says "Airline 3 did NOT have the least number of total delayed flights last year.". This is the same as saying that there must be at least one other Airline that have a smaller number of total delayed flights last year. Putting in a more mathy term, we want to evaluate as being true or not whether there is at least one k!=3, such that n_k*percentage_k_total < n_3*23%. We want something that must be true without any doubt, so lets find n_k < n_3 AND percentage_k_total < 23%, in a similar approach as done on statement 2:
- n_k < n_3: k = 4 or 5
- percentage_k_total < 23%: k = 4
So we can absolutelly say that Airline 3 did NOT have the least number of total delayed flights last year, because Airline 4 had less that Airline 3. (PS: note that we are not saying that Airline 4 had the least number, since we don't have enough information about how n_5 is smaller that n_4)

The question says had the greatest number of flights. We are only given percentages. The passage states that the airlines are in order from greatest number of fights (1) to least (5). What if Airline 1 had a 100,000 more flights than airline 2. Wouldn't matter now that airline 2 had a greater percentage. Thus, no conclusion can be made. 

­agreed. We are not given any absolute number but only a percentage. I ans is all question should be 'need not be true'
Anyone has clues? 
 

 

­Just seen this 'The airlines are numbered from greates total number of flights offered last year to least total number'

thank you

Here's a dumbed down explanation of why 2 and 3 are musts.
2. We know Airline 5 has the least number of passengers. Airline 5 also has the lowest percentage of delays over 60 minutes at 1.2%. Since both are the lowest, there must be the least number of delays.
3. We know Airline 4 and 5 had fewer number of passengers than Airline 3. If either had a fewer total delay % than Airline 3, then no matter what it would have fewer total delays than Airline 3. Since Airline 4 had a 20.3% total delay %, no matter what the number, Airline 4 will have fewer total delay %.
Logic:
WHAT WE ARE SOLVING FOR: Lower than Airline 3 passengers * Lower % total delays < Airline 3# passengers * 23%
Airline 4: Lower # passenger * 20.3%. Since Lower # passengers and 20.3% < 23%, the before statement is true in this case.
Airline 5: Lower # passengers * 24.9% We don't know.
Since Airline 4 is lower # passengers and lower % total delays, it MUST be lower than Airline 3.

Sajjad1994 this is a GMAT Prep Mock Question. Mock 2

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Note here that we do not know their total number of flights but we know that airline 1 had the maximum number of total flights and airline 5 had the minimum (in that order 1 to 5). 

Airline 2 had the greatest number of flights last year that were delayed by 1 to 15 minutes, to the nearest minute.

9.2% of all flights of Airline 2 were delayed by 1 to 15 minutes and that is the highest percentage but does it mean that it also represents the highest number of flights? No. What if Airline 2 had twice the number of total flights compared with airline 2 and so its 8.5% (number of flights that were delayed by 1 to 15 minutes) would be far more than those of airline 2.

ANSWER: Need not be true


Airline 5 had the least number of flights last year that were delayed by more than 60 minutes, to the nearest minute.

Airline 5 had only 1.2% flights delayed by more than 60 minutes, the lowest percentage among all airlines. We also know that airline 5 had the least total number of flights. This means 1.2% of the least total number of flights is bound to give us the least number of flights delayed by more than 60 minutes.

ANSWER: Must be true


Airline 3 did NOT have the least number of total delayed flights last year.

Airline 3 had 23% total flights delayed. Airline 4 has 20.3% of total flights delayed. The total number of flights of airline 4 were less than those of airline 3. So a lower percentage of a lower base will certainly lead to a lower number. So airline 4 certainly had fewer delayed flights last year compared with airline 3. Then we can say that definitely airline 3 did NOT have the least number of total delayed flights last year.

ANSWER: Must be true

Check this video on percentages: 
https://youtu.be/HxnsYI1Rws8